Abstract
In heavy-fermion compounds, f electrons show both itinerant and localized behaviour depending on the temperature1. Above a characteristic temperature, T*, their magnetic properties can be described by completely ‘localized’ f-electron models. On the other hand, well below T*, their Fermi surfaces can be explained by the ‘itinerant’ f-electron model2. These two models assume totally different natures of the f electrons, and how they transform between these states as a function of temperature has never been understood at the level of their electronic structures. Here, we use angle-resolved photoelectron spectroscopy to study the band structure of the heavy-fermion antiferromagnetic superconductor UPd2Al3 below and above T*, and find that the f bands, which form the Fermi surfaces at low temperatures, are excluded from the Fermi surfaces at high temperatures. This result demonstrates how the same f electrons can be both itinerant and localized.
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UPd2Al3 shows an antiferromagnetic transition at a Néel temperature of TN=14 K and undergoes a transition into the superconducting state at a critical temperature of Tc=2 K (ref. 3). Its Fermi surfaces at low temperatures were investigated by de Haas–van Alphen experiments4, and they were well explained by the itinerant 5f-electron model as described by band-structure calculations within the local density approximation5. At high temperatures, on the other hand, the magnetic susceptibility of UPd2Al3 follows the Curie–Weiss law above 50–70 K (ref. 6), suggesting almost completely localized magnetic moments at high temperatures. Therefore, 5f-electrons show either itinerant or localized properties depending on the temperature, and its crossover temperature T* is about 50–70 K. There are two explanations for this temperature dependence of the magnetic properties. One scenario is based on the conventional dense Kondo picture where the localized f moments at high temperatures are screened by a singlet coupling with the conduction electrons as the temperature decreases, and then condense into the itinerant heavy Fermi-liquid states at lower temperatures. The other is a two-component model, which assumes that one of the three U 5f electrons of one uranium atom is itinerant, whereas the remaining two electrons are localized7. The former gives itinerant properties at low temperatures, whereas the latter explains the localized magnetic properties at high temperatures3. The model further conjectures that the unconventional superconductivity in UPd2Al3 originates from the exchange interaction between these two subsystems. To determine how the U 5f electrons of UPd2Al3 can show both itinerant and localized properties, we have carried out angle-resolved photoelectron spectroscopy (ARPES) experiments in the soft X-ray region8,9 (SX-ARPES) at temperatures well below and above T* (20 and 100 K), and observed a remarkable temperature dependence of its band structure.
Figure 1a shows the angle-integrated photoemission (AIPES) spectra of UPd2Al3 measured with h ν=400 and 800 eV at 20 K. In this photon energy range, the contributions from the U 5f and Pd 4d states are dominant, and those from the Al 3s, 3p and U 6d states are one to two orders of magnitude smaller10. In Fig. 1a, we have also indicated the partial density of states (DOS) of the U 5f and the Pd 4d states obtained by a relativistic band-structure calculation within the local density approximation11. Comparison with the calculation suggests that the Pd 4d states are distributed mainly below the binding energy EB=3 eV and the U 5f states around the Fermi energy, EF. To extract contributions from the U 5f states, we have subtracted the spectrum measured at h ν=400 eV from that measured at h ν=800 eV, as shown in Fig. 1b, because the photoemission cross-section of the U 5f states relative to that of the Pd 4d states increases by a factor of two in going from h ν=400 eV to h ν=800 eV (ref. 10). The difference spectrum representing the U 5f distribution, as indicated by the blue line in Fig. 1b, shows a sharp peak just below EF, and a broad satellite structure extending to around EB=1.5 eV. In Fig. 1b, we compare the U 5f difference spectrum (blue line) with the calculated U 5f DOS broadened by the gaussian function representing the instrumental resolution (yellow line). As the observed sharp peak structure located around EF corresponds to the calculated DOS, this peak should originate from the itinerant quasiparticle bands. On the other hand, the broad satellite structure on the deeper binding energy side (EB>0.5 eV) cannot be explained by the band-structure calculation, suggesting that it might originate from the electron-correlation effect. In previous work12, it was proposed that this broad structure is the contribution from the completely localized U 5f2 subsystem. If this is the case, there should be only little energy dispersion, as has been observed in the ARPES spectra of the localized U 5f system UPd3 (ref. 13).
Figure 2c,d shows the hexagonal Brillouin zone of UPd2Al3 and the momentum position of the present ARPES cut measured at h ν=595 eV by the red curve. The present ARPES cut traces near the L–H–A high-symmetry line. In Fig. 2a, we show the density plot of the ARPES spectra measured at 20 K. In the near-EF part of the spectra, narrow quasiparticle bands of U 5f-state origin can be observed. On the other hand, some strongly dispersive bands can clearly be observed in the energy region of EB=0.5–1.0 eV, where the broad satellite structure is observed in the U 5f AIPES spectra. Therefore, the origin of the broad satellite structure in the AIPES spectra is the contribution not from less-dispersive localized U 5f states but from strongly dispersive bands with a finite contribution from U 5f states. In Fig. 2b, we show the results of the energy band calculation for the L–H–A direction, in which all of the U 5f electrons are treated as being itinerant. It is shown that some calculated bands correspond to the experimental bands. In particular, bands with large contributions from Pd 4d states located at EB>1.0 eV (band 14 and part of bands 15 and 16) agree with the ARPES spectra. On the other hand, the calculated bands with a large contribution from the U 5f states are different from the experimentally measured bands. For example, band 17 does not match with the experiment in the energy region of 0.2–0.5 eV. In the near-EF part of the spectra, the electron-like Fermi-surface feature around the A point shows agreement between experiment and calculation. On the other hand, a weak peak structure also remains at EF at other momentum positions, in disagreement with the calculation where the f-derived bands are far from EF except for around the H and A points. Therefore, U 5f states are strongly renormalized in the experiment, and they could not be well explained by the band-structure calculation.
Figure 3a shows a comparison of the ARPES spectra of UPd2Al3 measured at 20 and 100 K, which are sufficiently lower and higher than T* (∼50 K). Although the main structures of the spectra are very similar at 20 and 100 K, differences between them are clearly observed. The quasiparticle peaks located around EF show strong momentum dependence. When increasing the temperature from 20 to 100 K, their intensities are decreased around the H point, whereas they are increased around the A point. Meanwhile, the position of the quasiparticle peak uniformly moves towards slightly higher binding energy sides as the temperature is increased. Changes in spectral functions were also observed at higher binding energy sides. However, here we note that the changes in EB>1.5 eV are mainly changes in the peak intensity, and their positions are not changed, as described below. This suggests that they are not intrinsic changes in the electronic structures. We have further measured the temperature dependence of the ARPES spectra of UNi2Al3, whose characteristic temperature is higher than 300 K (ref. 14). Figure 3b shows a comparison of the ARPES spectra of UNi2Al3 measured at 20 and 100 K. It is clear that the spectra are not different at these two temperatures. Therefore, we conclude that the temperature dependence of the ARPES spectra of UPd2Al3 at around EB=EF−1.5 eV originates from the changes in the electronic structure of UPd2Al3 below and above T*.
To confirm the robustness of the temperature dependence and to study the temperature evolution of the spectra in more detail, we measured the ARPES spectra of UPd2Al3 at different positions in the Brillouin zone at smaller temperature intervals. Figure 4 shows the temperature evolution of the spectra, measured at 100, 60, 40 and 20 K. The spectra show similar temperature dependencies to those observed in Fig. 3a. In the near-EF part of the spectra, the peak position moves towards higher binding energies as the temperature increases. On the higher binding energy side, there are also substantial temperature dependencies. The spectra measured at 100 and 60 K show very similar structures, as do those measured at 40 and 20 K, whereas there are considerable differences between the two temperature ranges. Therefore, this temperature dependence with an abrupt change between 40 and 60 K is a robust feature of the ARPES spectra of UPd2Al3.
We further analyse the temperature dependence of the ARPES spectra shown in Fig. 3a. In Fig. 5a,b, we show the ARPES spectra measured at 20 and 100 K, which are divided by the Fermi–Dirac function convoluted with the gaussian function to reveal the behaviour of the quasiparticle bands in the vicinity of EF. The temperature dependence of the quasiparticle bands is clear in these figures. Furthermore, we have taken the second derivatives of the ARPES spectra to identify the peak positions in these spectra, as shown in Fig. 5c (20 K) and Fig. 5d (100 K). In these figures, the bright parts correspond to the peaks in the ARPES spectra. At 20 K, the quasiparticle bands below EF disperse to above EF, suggesting that they participate in the formation of the Fermi surfaces. On the other hand, at 100 K, they move towards the higher binding energy side, and form less dispersive bands around EB=0.1 eV. These changes imply that the quasiparticle bands of U 5f origin at low temperatures, which form the heavy Fermi-liquid states, are excluded from the Fermi surfaces at high temperatures. This behaviour of the quasiparticle bands is consistent with optical conductivity data, where the renormalized Drude peak and the hybridization gap due to the formation of the heavy quasiparticle bands are observed at T<50 K whereas the usual metallic behaviour with less Drude weight is observed at T>50 K (ref. 15). The usual metallic behaviour at T>50 K suggests that non-f bands form Fermi surfaces at high temperatures. However, their contributions cannot be clearly observed in these spectra as the lower energy parts of the spectra are dominated by strong U 5f contributions. These changes are consistent with the dense Kondo scenario, where the heavy quasiparticle bands are formed by hybridization between the flat renormalized f level located around EF and dispersive non-f bands16. On the other hand, the temperature-induced changes in the deeper binding energy region (EB<1 eV) can also be discerned in these figures. For example, around the areas designated as 1 in Fig. 5c,d, the structure located at EB=1 eV moves towards EB=1.1 eV in going from 20 to 100 K. In addition, the complicated band structures indicated in the areas designated as 2 also have significant temperature dependencies. This is in contrast to the changes at EB>1.2 eV, where the band structure was essentially unchanged at the two temperatures. Thus, the transition is accompanied by drastic changes in the band structure of an energy of the order of 1 eV (∼104 K), which is not expected in the theoretical prediction of the periodic Anderson model17. Therefore, the global nature of U 5f electrons of UPd2Al3 including the temperature dependence of the band structures cannot be explained by any of the current theories, and the present results provide a new scheme to describe the itinerant and localized nature of f electrons as well as the coexistence of magnetism and superconductivity in heavy-fermion compounds. Finally, we comment on the relationship between our study and other ARPES studies on heavy-fermion compounds. Although there have been several ARPES studies on heavy-fermion compounds, energy dispersions were not always clearly observed for the f levels18,19. One possible reason is that the measurements were done above T*, and therefore the coherence between the f sites was not developed in those experiments. In addition, those ARPES experiments were done with low-energy photons, and contributions from localized surface layers could not be ruled out. Therefore, we propose that low temperatures and reduced surface contributions are indispensable for detecting the energy dispersion of f-electron states in heavy-fermion compounds.
Methods
Photoemission experiment and data analysis
Photoemission experiments were carried out at the soft X-ray beamline BL23SU of SPring-8 (ref. 20) using a photoemission spectrometer equipped with a Gammadata-Scienta SES-2002 electron analyser. The AIPES spectra were measured using the angle-integrated mode of the spectrometer. The energy resolutions were 160 meV (h ν=800 eV) and 80 meV (h ν=400 eV). The energy and angular resolution of the SX-ARPES experiments were set to 120 meV and 0.16∘ (corresponding to 0.036 Å−1) respectively for a photon energy of 595 eV to obtain a reasonable count rate. The samples were cooled using a closed-cycle He refrigerator. The sample temperature was measured using a chromel–AuFe thermocouple mounted close to the sample. The base pressure of the spectrometer was better than 2×10−8 Pa. The position of the Fermi level was determined by the position of that of in situ evaporated gold film. The measured momentum positions were determined with a free-electron final-state model by taking the photon momentum into consideration. The momentum of the electron perpendicular to the surface with the free-electron final-state model is given by
where m is the electron mass, Ekin is the kinetic energy of the photoelectron, V0 is the inner potential, θ is the emission angle of the photoelectron relative to the surface normal and is the momentum of the incident photon perpendicular to the surface. We assumed that the inner potential was V0=12 eV, which is a typical value for heavy-fermion compounds19. To check the validity of the temperature dependencies of the ARPES spectra, we carried out different ARPES scans for a different UPd2Al3 single crystal, and confirmed that the temperature dependence of the ARPES spectra is reproducible. The sample orientation was measured ex situ using Laue photography. The image plots shown in Fig. 5c,d were obtained by adding the second derivative of the energy distribution curves with an appropriate weight to make the band images most clearly visible.
Sample preparation
The samples were characterized by X-ray diffraction. Lattice parameters at room temperature were determined to be a=5.368 Å and c=4.189 Å, in good agreement with previous studies21. The occupancy parameter at the Pd and Al sites was also refined to be 100% within an experimental accuracy of a few per cent. The direction of the crystal axes were determined using the Laue method. A clean sample surface was obtained by cleaving the sample in situ.
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Acknowledgements
We would like to acknowledge N. K. Sato, K. Miyake, N. Aso, G. Zwicknagl, G. H. Lander and A. Chainani for stimulating discussions and comments. This work was financially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology Japan under contract No.15740226 and REIMEI Research Resources from the Japan Atomic Energy Agency.
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Fujimori, SI., Saitoh, Y., Okane, T. et al. Itinerant to localized transition of f electrons in the antiferromagnetic superconductor UPd2Al3. Nature Phys 3, 618–622 (2007). https://doi.org/10.1038/nphys651
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DOI: https://doi.org/10.1038/nphys651